A Bayesian statistical inference method in which the prior distribution is estimated from the data
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Empirical Bayes methods are procedures for statistical inference in which the prior probability distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed before any data are observed. Despite this difference in perspective, empirical Bayes may be viewed as an approximation to a fully Bayesian treatment of a hierarchical model wherein the parameters at the highest level of the hierarchy are set to their most likely values, instead of being integrated out.[1] Empirical Bayes, also known as maximum marginal likelihood,[2] represents a convenient approach for setting hyperparameters, but has been mostly supplanted by fully Bayesian hierarchical analyses since the 2000s with the increasing availability of well-performing computation techniques. It is still commonly used, however, for variational methods in Deep Learning, such as variational autoencoders, where latent variable spaces are high-dimensional.
^Carlin, Bradley P.; Louis, Thomas A. (2002). "Empirical Bayes: Past, Present, and Future". In Raftery, Adrian E.; Tanner, Martin A.; Wells, Martin T. (eds.). Statistics in the 21st Century. Chapman & Hall. pp. 312–318. ISBN 1-58488-272-7.
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